About integration of solid angle

[KFC]

I am reading a book about integration on all possible momentum in 3D space, and it change the integration to a 1D integration and integration on solid angle, I don't know how does it happen

<br /> \int d^3p \to \int p^2dp\int d\Omega<br />

where \Omega is the solid angle.

 

[adriank]

Work in spherical coordinates (p, \theta, \phi), so that d^3 \vec p = p^2 \sin \theta \,dp \,d\theta \,d\phi, and note that the definition of solid angle is d\Omega = \sin \theta \,d\theta \,d\phi.